Blangiardo and Cameletti (2015) section 4.9
The posterior distribution of the nuisance parameter is
\[p(\psi|\mathbf{y}) \propto \frac{p(\mathbf{y} | \theta, \psi) p(\theta) p(\psi)} {p(\theta | \psi, \mathbf{y})}\]
bei dataset in spatstat (Baddeley and Turner 2005)inlabru has a nice interface but is slow and poorly documentedBaddeley, Adrian, and Rolf Turner. 2005. “Spatstat: An R Package for Analyzing Spatial Point Patterns.” Journal of Statistical Software 12 (6): 1–42.
Blangiardo, Marta, and Michela Cameletti. 2015. Spatial and Spatio-Temporal Bayesian Models with R-INLA. Wiley.
Johnson, Devin, Jeff Laake, and Jay VerHoef. 2014. DSpat: Spatial Modelling for Distance Sampling Data. https://CRAN.R-project.org/package=DSpat.
Møller, J, and RP Waagepetersen. 2007. “Modern Spatial Point Process Modelling and Inference.” Scandinavian Journal of Statistics 34: 643–711.
Rue, Håvard, Sara Martino, and Nicolas Chopin. 2009. “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 71 (2): 319–92.
Simpson, Daniel, Janine B Illian, Finn Lindgren, Sigrunn H Sørbye, and Havard Rue. 2016. “Going Off Grid: Computationally Efficient Inference for Log-Gaussian Cox Processes.” Biometrika 103 (1): 49–70.
Yuan, Yuan, Fabian E Bachl, Finn Lindgren, David L Borchers, Janine B Illian, Stephen T Buckland, Haavard Rue, Tim Gerrodette, and others. 2017. “Point Process Models for Spatio-Temporal Distance Sampling Data from a Large-Scale Survey of Blue Whales.” The Annals of Applied Statistics 11 (4): 2270–97.